Roever — Geometrical Constructions of Lines of Force. 211 



of parallelism the point of intersection is below A' A, and the 

 part marked 2 is traced. This part necessarily has the same 

 asymptote as part 1. The point A on part 2 is reached when 

 the line A'P makes an angle tt with A' A, and then the line 

 AP is tangent to part 2 at A. On further rotation the part 3 

 of a loop is traced. The point A on this loop is reached 



when AP makes an angle tt with AO, and then AP is tan- 

 gent to part 3 at A' . Next the part 4 of the loop below A' A 

 is traced; the point A is reached when AP again coincides 

 with A A, and then AP is tangent to part 4 at A. Next 

 part 5, which approaches asymptote II, is traced. After this 

 second position of parallelism part 6 is traced, then part 7, 

 and so on in the order indicated by the numbers. Any two 

 consecutive asymptotes, as for instance III and /F, are not, 

 in general, adjacent. 



The equation of the curve in Fig. 5 is 



5 20 



8ft) 3&)' — 8 Jo TT — -^ "^t 



